I voted this down simply based on the fact that this site should be for expert level Q&A, not extremely basic questions that are answered by your manual or the spec sheet of a product. Although I did answer the question so you will have an answer to help you out.
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dpollittMay 27 '13 at 21:43

expert level? I sure see a lot of beginner questions that are trivially answered by a FAQ, manual, or spec sheet. Are you perhaps being a bit rough on the rookie?
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Pat FarrellJun 30 '13 at 21:06

4 Answers
4

Assuming you are referring to the Nikon AF-S DX NIKKOR
55-300mm f/4.5-5.6G ED VR - Yes of course it will work. The Nikon D5200 is a DX format camera with an F-Mount, and this is a DX format F-Mount lens. The D5200 does not have an autofocus motor built into it, but any lens that is "AF-S" has it built into the lens. So this lens will autofocus on the D5200.

The Nikkor 55-300mm f/4.5-5.6G DX lens was a bit of a surprise when it was announced, as Nikon already had two very good telephoto zooms that appealed to DX body users (55-200mm DX and 70-300mm VR). Why Nikon was revisiting the low-cost telephoto space before filling out other DX options had a lot of Nikon users puzzled. Still, with two low-cost cameras (D3100, D5100) in the lineup, having low-cost lenses for them seems like the right thing to me. The question at hand is whether this was the right addition to the low cost lineup.

This is interesting background, but actually, the "question at hand" is simply whether this lens will work on a D5200. More info is great, but please do at least answer the question -- this is a Q&A site, not a discussion forum!
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mattdmDec 15 '13 at 9:32

Yes, It will.
DX means the same format your camera is made for.
AF-s means the lens has an auto focus motor in it. as your camera does not have a built-in auto focus system, this lens will work perfectly.